2017/02/28 by Ovidiu Cristinel Stoica · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Clifford algebra #Electroweak interaction #Lepton #Mathematics #Muon and positron interactions and applications #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Quark #hep-th #math-ph #math.MP #math.RT
paper · pdf · doi:10.1007/s00006-018-0869-4
published as Adv. Appl. Clifford Algebras (2018) 28: 52
openalex publication_date 2018/05/04 · crossref created 2018/05/04 · crossref issued 2018/05/05 · crossref published 2018/05/05 · crossref published-online 2018/05/05 · arxiv created 2018/05/08 · arxiv updated 2018/05/10 · crossref published-print 2018/07/01 · crossref deposited 2019/05/06 · openalex created_date 2021/02/01 · crossref indexed 2026/06/04 · openalex updated_date 2026/07/29
A simple geometric algebra is shown to contain automatically the leptons and quarks of a family of the Standard Model, and the electroweak and color gauge symmetries, without predicting extra particles and symmetries. The algebra is already naturally present in the Standard Model, in two instances of the Clifford algebra ℂℓ6, one being algebraically generated by the Dirac algebra and the weak symmetry generators, and the other by a complex three-dimensional representation of the color symmetry, which generates a Witt decomposition which leads to the decomposition of the algebra into ideals representing leptons and quarks. The two instances being isomorphic, the minimal approach is to identify them, resulting in the model proposed here. The Dirac and Lorentz algebras appear naturally as subalgebras acting on the ideals representing leptons and quarks. The resulting representations on the ideals are invariant to the electromagnetic and color symmetries, which are generated by the bivectors of the algebra. The electroweak symmetry is also present, and it is already broken by the geometry of the algebra. The model predicts a bare Weinberg angle θW given by sin2θW=0.25. The model shares common ideas with previously known models, particularly with Chisholm and Farwell, 1996, Trayling and Baylis, 2004, and Furey, 2016.